ive noticed quite a few posts on here with the question of how to deal with painted surfaces, so I thought I woulld give a master decorators perspective to this

newly plastered walls are given a chance to dry out before being given a light sanding. this smooths and removes the polish left by the plasteres trowel
the walls are then sealed with a mist coat, this is a trade quality matt emulsion[not vinyl] thinned with up to 40% water

once dry this acts as a seal and a primer for the subsequent coats, two or more thinned coats are applied, the paint can be thinned with up to 20% water

this paint is now properly applied and wont peel , flake etc and you wont strip it, however if you tile it as it is you are relying on the bond of the paint to the wall to support the weight of your addy and tiles

the way to deal with this is to sand it till you can see the plaster surface showing through, you will then be bonding to the sealed plaster not the paint

thats a new buildbut an older property has been redecorated many times and this is where the problems for a tiler start

the correct way to redecorate is to sand the old paint to remove the dirty , greasy surface, thin your paint with up to 20% water and coat with a minimum of 2 coats. how many professional decorators do this let alone diyers, a full coat over the existing dirt and grease leaves a weak bond between the paint layers, this will debond if tiled over

the other problem is that while the new plaster was painted with a matt emulsion to allow the walls to dry and breathe .subsequent coats are likely to be vinyl emulsion [which does come in a matt finish] or specific bathroom paint which has a vinyl base

this paint cannot be tiled over and has to be removed, the most effective way of removing vinyl based emulsion is with a steam stripper, failing that its an unpleasant job with the sander

but it does have to be removed before tiling

instead of stripping/sanding you could also put up new plasterboard/cement board of ten v-easy